Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D688 | C2 | semidirect |
| 2. C2×#14583315 | C2 | semidirect |
| 3. #19144244 | C2 | semidirect |
| 4. #19136699 | C2 | semidirect |
| 5. #19136682 | C2 | semidirect |
| 6. #19136310 | C2 | semidirect |
| 7. C43×#2158 | C2 | semidirect |
| 16. C2×#13063264 | C22 | semidirect |
| 17. C2×C16×D43 | C22 | semidirect |
| 19. #14583136 | C22 | semidirect |
| 21. #14582699 | C22 | semidirect |
| 24. C43×#367 | C22 | semidirect |
| 25. C43×#366 | C22 | semidirect |
| 50. C2×C16×C43 | D4 | semidirect |
| 130. #2158 | D43 | semidirect |
| 152. #367 | C2×D43 | semidirect |
| 153. #366 | C2×D43 | semidirect |
| 155. C43 | #33607 | semidirect |
| 179. C2×C16 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D688 | 2 |
| C2×#14583315 | 2 |
| #19144244 | 2 |
| #19136699 | 2 |
| #19136682 | 2 |
| #19136310 | 2 |
| C43×#2158 | 2 |
| #33607 | 43 |